\documentclass{article}
\usepackage{pgfplots}
\usepackage{amsmath}
\usepackage{ctex}
\pgfplotsset{compat=1.18}

\begin{document}

于是最终 $\sin(x)$ 的 2/2 阶帕德逼近为：
\[
R_{2,2}(x)=\frac{x}{1+\frac{1}{6}x^{2}}
\]

在坐标系上，帕德逼近和原函数在越接近于 0 的地方误差越小，离 0 越远误差越大，图像如下：

\begin{center}
\begin{tikzpicture}
\begin{axis}[
    axis lines = middle,
    xlabel = $x$,
    ylabel = $y$,
    xmin = -4, xmax = 4,
    ymin = -3, ymax = 3,
    xtick = {-4,-3,-2,-1,0,1,2,3,4},
    ytick = {-3,-2,-1,0,1,2,3},
    width=10cm, height=7cm,
    samples=200,
    domain=-4:4,
    thick,
    legend style={at={(0.5,-0.15)},anchor=north,legend columns=2}
]

% 正弦函数 sin(x) —— 绿色
\addplot[green, thick] {sin(deg(x))};

% 帕德逼近 R_{2,2}(x) —— 蓝色
\addplot[blue, thick] {x / (1 + (1/6)*x^2)};

\legend{$\sin(x)$, $R_{2,2}(x)$}
\end{axis}
\end{tikzpicture}
\end{center}

\end{document}
